He may have considered joining an existing Presbyterian group before founding the Orthodox Presbyterian Church - it would be surprising if he had not - but if he never wrote about such thoughts, it will be almost impossible to answer this question. Well, not unless he did write something along the lines of, 'Having been defrocked in 1936, I now have no choice but to found a new denomination.' (And bear in mind that he died in 1937.) From that we might suppose he had been considering joining an existing group, but being defrocked put paid to such considerations. Yet that is only supposition.
However, there is something he wrote in his book (below) that indicates a great resistance to joining any group that did not fully subscribe to the Westminster Confession of Faith, which he took to be formed on the basis of the binding authority of Holy Scripture. This would mean that if the Presbyterian denominations you mentioned - the PCUS (in the South), the ARP, and the RPCNA - did not hold firmly to that particular Confession, the Professor would have been most unlikely to have considered them. This is what he wrote about American Presbyterianism in its moving away from the binding authority of Holy Scripture:
"...a man who solemnly accepts that system of doctrine [viz. the
Westminster Confession] cannot at the same time be an advocate of a
non-doctrinal religion which regards as a trifling thing that which is
the very sum and substance of the Confession and the very centre and
core of the Bible upon which it is based."
"The matter may be made plain by an illustration from secular life.
Suppose in a political campaign in America there be formed a
Democratic Club for the purpose of furthering the cause of the
Democratic Party. Suppose there are certain other citizens who are
opposed to the tenets of the Democratic Club, and in opposition desire
to support the Republican Party. What is the honest way for them to
accomplish this purpose? Plainly, it is simply the formation of a
Republican Club which shall carry on propaganda in favour of
Republican principles. But suppose instead of pursuing this simple
course of action, the advocates of Republican principles should
conceive the notion of making a declaration of conformity to
Democratic principles, thus gaining entrance into an anti-Democratic
propaganda. That plan might be ingenious. But would it be honest? Yet
it is exactly such a plan which is adopted by advocates of a
non-doctrinal religion who by subscription to a creed gained an
entrance into the ministry of doctrinal or evangelical Churches."
Christianity and Liberalism, p.169, J.G. Machen (as quoted in The Heritage of our Fathers, p.86, G.N.M. Collins, The Knox Press, 1974)
This is by no means conclusive, but it appears to be a conclusion he arrived at which, while not ruling out Machen considering joining other Presbyterian denominations, would mitigate against supposing that he seriously would join one that did not hold utterly to the binding authority of Holy Scripture as expressed in the Westminster Confession.
